For a number of years it has been noticed by a variety of researchers that adaptive filtering algorithms such as (Normalized) Least-Mean-Squares (NLMS) do not always behave as expected for the corresponding Wiener filter.
FIG. 1 illustrates a prior art adaptive filter that uses only one channel, the reference channel, that receives a reference signal rn as input to the linearly combining adaptive filter. The performance of such an adaptive filter, in a stationary environment, is well known and limited to the performance of a two-channel Wiener filter. The adaptive filter depicted in FIG. 1 also employs a primary signal dn in conjunction with the reference signal rn for determining an error signal en. However, the prior art adaptive filter, while possibly doing better than its Wiener filter counterpart, cannot generally achieve the limiting performance due to the time-varying nature of the optimal reference-only filter. Therefore, a need exists for an adaptive filter that can approach the limiting performance, and thereby overcome the limitations of prior art adaptive filters.
Throughout the several views, like elements are referenced using like references.